They have already shown that Khan was not an adult in the 21st century and that the Eugenics Wars didn't take place in 1999, so if that was an intersection point in the same timeline, SNW is not the same timeline as Space Seed. It is likely the same timeline as Picard though, but that's the point I was making - The Naked Time, CotEoF, the Voyage Home, Yesterday's Enterprise, Past Tense, Trials & Tribbleations, All Good Things, First Contact, Year of Hell, Timeless, and Magic to Make the Sanest Man Go Mad, all potentially shift the viewer into a different parallel timeline from where we started at the beginning of that episode (I say potentially because this is only true if the episode starts out in the universe that we watched in the previous episode and in the Harry Mudd episode, that seem unlikely and also it is implied that the Voyage Home is a closed loop). I think as viewers, we are supposed to assume that every other character everywhere else is the same as when we last saw them, even though we are in a different timeline but that doesn't have to be the case.